Tutorial

  • 2021.4
  • 09/27/2021
  • Public Content

Multiplying Matrices Using dgemm

oneMKL
provides several routines for multiplying matrices. The most widely used is the
dgemm
routine, which calculates the product of double precision matrices:
The
dgemm
routine can perform several calculations. For example, you can perform this operation with the transpose or conjugate transpose of
A
and
B
. The complete details of capabilities of the
dgemm
routine and all of its arguments can be found in the
?gemm
topic in the
Intel® oneAPI
Math Kernel Library
Developer Reference
.

Use dgemm to Multiply Matrices

This exercise demonstrates declaring variables, storing matrix values in the arrays, and calling
dgemm
to compute the product of the matrices. The arrays are used to store these matrices:
The one-dimensional arrays in the exercises store the matrices by placing the elements of each column in successive cells of the arrays.
The Fortran source code for this tutorial is shown below.
Although
oneMKL
supports Fortran 90 and later, the exercises in this tutorial use FORTRAN 77 for compatibility with as many versions of Fortran as possible.
* Fortran source code is found in dgemm_example.f PROGRAM MAIN IMPLICIT NONE DOUBLE PRECISION ALPHA, BETA INTEGER M, K, N, I, J PARAMETER (M=2000, K=200, N=1000) DOUBLE PRECISION A(M,K), B(K,N), C(M,N) PRINT *, "This example computes real matrix C=alpha*A*B+beta*C" PRINT *, "using Intel(R) MKL function dgemm, where A, B, and C" PRINT *, "are matrices and alpha and beta are double precision " PRINT *, "scalars" PRINT *, "" PRINT *, "Initializing data for matrix multiplication C=A*B for " PRINT 10, " matrix A(",M," x",K, ") and matrix B(", K," x", N, ")" 10 FORMAT(a,I5,a,I5,a,I5,a,I5,a) PRINT *, "" ALPHA = 1.0 BETA = 0.0 PRINT *, "Intializing matrix data" PRINT *, "" DO I = 1, M DO J = 1, K A(I,J) = (I-1) * K + J END DO END DO DO I = 1, K DO J = 1, N B(I,J) = -((I-1) * N + J) END DO END DO DO I = 1, M DO J = 1, N C(I,J) = 0.0 END DO END DO PRINT *, "Computing matrix product using Intel(R) MKL DGEMM " PRINT *, "subroutine" CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M) PRINT *, "Computations completed." PRINT *, "" PRINT *, "Top left corner of matrix A:" PRINT 20, ((A(I,J), J = 1,MIN(K,6)), I = 1,MIN(M,6)) PRINT *, "" PRINT *, "Top left corner of matrix B:" PRINT 20, ((B(I,J),J = 1,MIN(N,6)), I = 1,MIN(K,6)) PRINT *, "" 20 FORMAT(6(F12.0,1x)) PRINT *, "Top left corner of matrix C:" PRINT 30, ((C(I,J), J = 1,MIN(N,6)), I = 1,MIN(M,6)) PRINT *, "" 30 FORMAT(6(ES12.4,1x)) PRINT *, "Example completed." STOP END
This exercise illustrates how to call the
dgemm
routine. An actual application would make use of the result of the matrix multiplication.
This call to the
dgemm
routine multiplies the matrices:
CALL DGEMM('N','N',M,N,K,ALPHA,A,M,B,K,BETA,C,M)
The arguments provide options for how
oneMKL
performs the operation. In this case:
'N'
Character
indicating that the matrices
A
and
B
should not be transposed or conjugate transposed before multiplication.
M, N, K
Integers indicating the size of the matrices:
  • A
    :
    M
    rows by
    K
    columns
  • B
    :
    K
    rows by
    N
    columns
  • C
    :
    M
    rows by
    N
    columns
ALPHA
Real value used to scale the product of matrices
A
and
B
.
A
Array used to store matrix
A
.
M
Leading dimension of array
A
, or the number of elements between successive
columns (for column major storage)
in memory. In the case of this exercise the leading dimension is the same as the number of
rows
.
B
Array used to store matrix
B
.
K
Leading dimension of array
B
, or the number of elements between successive
columns (for column major storage)
in memory. In the case of this exercise the leading dimension is the same as the number of
rows
.
BETA
Real value used to scale matrix
C
.
C
Array used to store matrix
C
.
M
Leading dimension of array
C
, or the number of elements between successive
columns (for column major storage)
in memory. In the case of this exercise the leading dimension is the same as the number of
rows
.

Compile and Link Your Code

oneMKL
provides many options for creating code for multiple processors and operating systems, compatible with different compilers and third-party libraries, and with different interfaces. To compile and link the exercises in this tutorial with Intel® Parallel Studio XE Composer Edition, type
  • Windows* OS:
    ifort /Qmkl src\dgemm_example.f
  • Linux* OS, macOS*:
    ifort -mkl src/dgemm_example.f
Alternatively, you can use the supplied build scripts to build and run the executables.
  • Windows* OS:
    build build run_dgemm_example
  • Linux* OS, macOS*:
    make make run_dgemm_example
For the executables in this tutorial, the build scripts are named:
Example
Executable
dgemm_example
.f
run_dgemm_example
dgemm_with_timing
.f
run_dgemm_with_timing
matrix_multiplication
.f
run_matrix_multiplication
dgemm_threading_effect_example
.f
run_dgemm_threading_effect_example
This assumes that you have installed
oneMKL
and set environment variables as described in .
For other compilers, use the
oneMKL
Link Line Advisor to generate a command line to compile and link the exercises in this tutorial: http://software.intel.com/en-us/articles/intel-mkl-link-line-advisor/.
After compiling and linking, execute the resulting executable file, named
dgemm_example.exe
on Windows* OS or
a.out
on Linux* OS and macOS*.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.